He added: "I'd just say that this man is not Christian if he said it this way."
Trump, a Presbyterian who has promised to deport millions of undocumented immigrants and build a wall along the U.S-Mexico border, strongly rebuked the pope's comments.
"For a religious leader to question a person's faith is disgraceful," the Republican presidential front-runner said at a campaign rally in South Carolina. "I'm proud to be a Christian, and as president I will not allow Christianity to be consistently attacked and weakened, unlike what is happening now with our current president."
Trump's critics have accused him of racism and xenophobia and of disregarding the destitute economic conditions that many undocumented immigrants have fled. But his positions on immigration have been at the core of the real estate mogul's pitch to supporters, who believe political leaders have not done enough to protect American interests at home and abroad.
About eight minutes into his 45-minute speech here Thursday, Trump declared that "Mexico is the new China" and used the pope's just-concluded visit as an example.
"The pope was in Mexico," Trump said. "Do you know that? Does everyone know that? He said negative things about me because the Mexican government convinced him that Trump is not a good guy because I want to have a strong border, I want to stop illegal immigration, I want to stop people from being killed."
He continued: "The Mexican government fed the pope a tremendous amount of stuff about 'Trump is not a good person'.... Can you imagine that?"
Mexican officials, he added, were "using the pope as a pawn."
"The pope only heard one side of the story," Trump said.
Trump said he received a call about the pope's comments on his way to the rally. The crowd laughed as Trump acted out his response.
"As I'm walking up here, they said: 'Mr. Trump, the pope made a statement about you. I said: 'The pope?' I said: 'I like the pope.... Was it good or bad, because if it's good, I like the pope."
It was not good, Trump noted.
"He actually said it, that maybe I'm not a good Christian or something — it's unbelievable — which is really not a nice thing to say."
He indicated that the pope would change his mind if the Vatican were attacked by Islamic State terrorists.
“If and when the Vatican is attacked by ISIS, which as everyone knows is ISIS’s ultimate trophy, I can promise you that the pope would have only wished and prayed that Donald Trump would have been president,” Trump said, reading from a statement. “ISIS would have been eradicated unlike what is happening now with our all-talk, no-action politicians.”
A senior Trump adviser took to Twitter on Thursday to note that a wall already exists around Vatican City.
In late 2013, on that same social media platform, Trump spoke favorably of Francis.
In addressing the pope's remarks Thursday, Trump reiterated his call for a wall on the U.S.-Mexico border.
He also defended his faith, saying: "I am Christian. I'm proud of it."
A mention of protecting Christianity drew cheers.
Trump's comments came three days after he criticized rival Ted Cruz for how the senator from Texas invoked his Christian faith during the campaign. During an appearance before activists in South Carolina on Monday, Trump argued that he would be the better guardian of Christian values, before saying: "Christianity is being chopped away at. Chop, chop, chop."
Cruz has also supported building a wall along the U.S.-Mexico border, saying in December: "We will build a wall that works, and I'll get Donald Trump to pay for it."
As he boarded his campaign bus Thursday afternoon in Greenville, S.C., Cruz did not respond to questions yelled at him by reporters about the pope's comments.
In Anderson, S.C., another Republican candidate, Sen. Marco Rubio of Florida, said he had not seen "the pope's statement in its full context."
But, Rubio said, "there is no nation on Earth that is more compassionate ... on immigration than we are. We accept a million people a year in the United States, legally, every year. Mexico doesn’t do that. No other country in the world does that. We’re a sovereign country. We have a right to control who comes in, when they come in and how they come in. Vatican City controls who comes in, when they come in and how they come in as a city-state."
Campaigning in another part of the state, Jeb Bush said it was improper for the pope to question Trump's faith.
"I think his Christianity is between him and his creator," Bush told reporters. "I don't think we need to discuss that."
Another contender, Ohio Gov. John Kasich, spent five full minutes praising Pope Francis Thursday when he was asked about his comments on Trump. Kasich stressed that he believes the pope was not actually saying Trump is not a Christian.
“I love the pope,” the Ohio governor said after a town hall meeting sponsored by Clemson University’s Strom Thurmond Institute. “The pope, in terms of his overall message has been one of love and compassion."
Following Trump's rally Thursday, one 65-year-old Catholic said the pope was "becoming too political."
"I'm against what he's doing," said Kathy Hogan, a retired economics teacher who lives in Kiawah Island. "I understand he's a very holy man, but I think he needs to stay out of politics."
As Trump sat down for lunch at Fratellos Italian Tavern in North Charleston with Mayor R. Keith Summey, who had just endorsed him, Summey brought up the pope's comments.
"I don't care if he's the pope or not, you know, the bottom line is: Your faith is your faith," Summey said. "And for someone to question it because they disagree with something you say -- that's getting back to where the fight which you have among the different faiths in the world. I mean, I'm a Baptist but I think there are some darn good Catholics and darn good Jews, a lot of good people out there in this country, and just because I say something they disagree with doesn't mean that I have any less faith than they have."
As the mayor spoke, Trump listened quietly with his lips tightly pressed together. "It's a very sad situation," Trump said.
Trump later told reporters he has no plan to reach out to the pope.
One reporter pointed out that South Carolina is one of the least Catholic states in the country, with one of the smallest percentages of Catholic residents and asked if that factored into his comments.
"I don't even think about that," Trump said. "I have no idea what the percentages are. I just know that I speak the truth. I don't go to pollsters.... I thought that it was inappropriate."
Trump was also asked if he is still respectful of the pope. "Totally respectful -- absolutely," he said.
Speaking in both Spanish and Italian on the flight home from Mexico, Francis struck a different tone when he was asked about the debate over civil unions in Italy.
"The pope doesn’t get mixed up in Italian politics," he said, according to a Catholic News Agency transcript. Francis added that "the pope is for everybody and he can’t insert himself in the specific internal politics of a country. This is not the role of the pope, right?"
DelReal reported from Columbia, S.C., and du Lac from Washington. Sean Sullivan, Katie Zezima, Mark Berman, James Hohmann and Ed O'Keefe contributed to this post, which has been updated.